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I have following data and I want apply regression analysis for this data.Based on the data I want derive equation of 2nd or 3rd or 4th order polynomial equation. How can I do that by using math concept and later I want implement it using python.

[[161.2, 51.6], [167.5, 59.0], [159.5, 49.2], [157.0, 63.0], [155.8, 53.6],
            [170.0, 59.0], [159.1, 47.6], [166.0, 69.8], [176.2, 66.8], [160.2, 75.2],
            [172.5, 55.2], [170.9, 54.2], [172.9, 62.5], [153.4, 42.0], [160.0, 50.0],
            [147.2, 49.8], [168.2, 49.2], [175.0, 73.2], [157.0, 47.8], [167.6, 68.8],
            [159.5, 50.6], [175.0, 82.5], [166.8, 57.2], [176.5, 87.8], [170.2, 72.8],
            [174.0, 54.5], [173.0, 59.8], [179.9, 67.3], [170.5, 67.8], [160.0, 47.0],
            [154.4, 46.2], [162.0, 55.0], [176.5, 83.0], [160.0, 54.4], [152.0, 45.8],
            [162.1, 53.6], [170.0, 73.2], [160.2, 52.1], [161.3, 67.9], [166.4, 56.6],
            [168.9, 62.3], [163.8, 58.5], [167.6, 54.5], [160.0, 50.2], [161.3, 60.3],
            [167.6, 58.3], [165.1, 56.2], [160.0, 50.2], [170.0, 72.9], [157.5, 59.8],
            [167.6, 61.0], [160.7, 69.1], [163.2, 55.9], [152.4, 46.5], [157.5, 54.3],
            [168.3, 54.8], [180.3, 60.7], [165.5, 60.0], [165.0, 62.0], [164.5, 60.3],
            [156.0, 52.7], [160.0, 74.3], [163.0, 62.0], [165.7, 73.1], [161.0, 80.0],
            [162.0, 54.7], [166.0, 53.2], [174.0, 75.7], [172.7, 61.1], [167.6, 55.7],
            [151.1, 48.7], [164.5, 52.3], [163.5, 50.0], [152.0, 59.3], [169.0, 62.5],
            [164.0, 55.7], [161.2, 54.8], [155.0, 45.9], [170.0, 70.6], [176.2, 67.2],
            [170.0, 69.4], [162.5, 58.2], [170.3, 64.8], [164.1, 71.6], [169.5, 52.8],
            [163.2, 59.8], [154.5, 49.0], [159.8, 50.0], [173.2, 69.2], [170.0, 55.9],
            [161.4, 63.4], [169.0, 58.2], [166.2, 58.6], [159.4, 45.7], [162.5, 52.2],
            [159.0, 48.6], [162.8, 57.8], [159.0, 55.6], [179.8, 66.8], [162.9, 59.4],
            [161.0, 53.6], [151.1, 73.2], [168.2, 53.4], [168.9, 69.0], [173.2, 58.4],
            [171.8, 56.2], [178.0, 70.6], [164.3, 59.8], [163.0, 72.0], [168.5, 65.2],
            [166.8, 56.6], [172.7, 105.2], [163.5, 51.8], [169.4, 63.4], [167.8, 59.0],
            [159.5, 47.6], [167.6, 63.0], [161.2, 55.2], [160.0, 45.0], [163.2, 54.0],
            [162.2, 50.2], [161.3, 60.2], [149.5, 44.8], [157.5, 58.8], [163.2, 56.4],
            [172.7, 62.0], [155.0, 49.2], [156.5, 67.2], [164.0, 53.8], [160.9, 54.4],
            [162.8, 58.0], [167.0, 59.8], [160.0, 54.8], [160.0, 43.2], [168.9, 60.5],
            [158.2, 46.4], [156.0, 64.4], [160.0, 48.8], [167.1, 62.2], [158.0, 55.5],
            [167.6, 57.8], [156.0, 54.6], [162.1, 59.2], [173.4, 52.7], [159.8, 53.2],
            [170.5, 64.5], [159.2, 51.8], [157.5, 56.0], [161.3, 63.6], [162.6, 63.2],
            [160.0, 59.5], [168.9, 56.8], [165.1, 64.1], [162.6, 50.0], [165.1, 72.3],
            [166.4, 55.0], [160.0, 55.9], [152.4, 60.4], [170.2, 69.1], [162.6, 84.5],
            [170.2, 55.9], [158.8, 55.5], [172.7, 69.5], [167.6, 76.4], [162.6, 61.4],
            [167.6, 65.9], [156.2, 58.6], [175.2, 66.8], [172.1, 56.6], [162.6, 58.6],
            [160.0, 55.9], [165.1, 59.1], [182.9, 81.8], [166.4, 70.7], [165.1, 56.8],
            [177.8, 60.0], [165.1, 58.2], [175.3, 72.7], [154.9, 54.1], [158.8, 49.1],
            [172.7, 75.9], [168.9, 55.0], [161.3, 57.3], [167.6, 55.0], [165.1, 65.5],
            [175.3, 65.5], [157.5, 48.6], [163.8, 58.6], [167.6, 63.6], [165.1, 55.2],
            [165.1, 62.7], [168.9, 56.6], [162.6, 53.9], [164.5, 63.2], [176.5, 73.6],
            [168.9, 62.0], [175.3, 63.6], [159.4, 53.2], [160.0, 53.4], [170.2, 55.0],
            [162.6, 70.5], [167.6, 54.5], [162.6, 54.5], [160.7, 55.9], [160.0, 59.0],
            [157.5, 63.6], [162.6, 54.5], [152.4, 47.3], [170.2, 67.7], [165.1, 80.9],
            [172.7, 70.5], [165.1, 60.9], [170.2, 63.6], [170.2, 54.5], [170.2, 59.1],
            [161.3, 70.5], [167.6, 52.7], [167.6, 62.7], [165.1, 86.3], [162.6, 66.4],
            [152.4, 67.3], [168.9, 63.0], [170.2, 73.6], [175.2, 62.3], [175.2, 57.7],
            [160.0, 55.4], [165.1, 104.1], [174.0, 55.5], [170.2, 77.3], [160.0, 80.5],
            [167.6, 64.5], [167.6, 72.3], [167.6, 61.4], [154.9, 58.2], [162.6, 81.8],
            [175.3, 63.6], [171.4, 53.4], [157.5, 54.5], [165.1, 53.6], [160.0, 60.0],
            [174.0, 73.6], [162.6, 61.4], [174.0, 55.5], [162.6, 63.6], [161.3, 60.9],
            [156.2, 60.0], [149.9, 46.8], [169.5, 57.3], [160.0, 64.1], [175.3, 63.6],
            [169.5, 67.3], [160.0, 75.5], [172.7, 68.2], [162.6, 61.4], [157.5, 76.8],
            [176.5, 71.8], [164.4, 55.5], [160.7, 48.6], [174.0, 66.4], [163.8, 67.3]]
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  • $\begingroup$ Are you asking how to decide among the polynomial orders? Could you explain why you think you need a polynomial model specifically? The mechanics of regression, including polynomial regression, are extensively covered elsewhere on this site, so if that's your interest, just browse our regression answers or (better) search the site using the obvious keywords such as "polynomial" and "regression". $\endgroup$ – whuber Mar 18 '16 at 14:45
  • $\begingroup$ No, I have data as mentioned above, for that I want derive regression equation by applying polynomial model. $\endgroup$ – niran Mar 18 '16 at 14:48
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    $\begingroup$ ... and for the equations of multiple regression, see stats.stackexchange.com/… $\endgroup$ – whuber Mar 18 '16 at 14:50